TY - JOUR
T1 - Port-Hamiltonian Modeling of Ideal Fluid Flow
T2 - Part II. Compressible and Incompressible Flow
AU - Rashad, Ramy
AU - Califano, Federico
AU - Schuller, Frederic P.
AU - Stramigioli, Stefano
N1 - Funding Information:
This work was supported by the PortWings project funded by the European Research Council [Grant Agreement No. 787675]
Publisher Copyright:
© 2021 The Author(s)
PY - 2021/6
Y1 - 2021/6
N2 - Part I of this paper presented a systematic derivation of the Stokes Dirac structure underlying the port-Hamiltonian model of ideal fluid flow on Riemannian manifolds. Starting from the group of diffeomorphisms as a configuration space for the fluid, the Stokes Dirac structure is derived by Poisson reduction and then augmented by boundary ports and distributed ports. The additional boundary ports have been shown to appear naturally as surface terms in the pairings of dual maps, always neglected in standard Hamiltonian theory. The port-Hamiltonian model presented in Part I corresponded only to the kinetic energy of the fluid and how its energy variables evolve such that the energy is conserved. In Part II, we utilize the distributed port of the kinetic energy port-Hamiltonian system for representing a number of fluid-dynamical systems. By adding internal energy we model compressible flow, both adiabatic and isentropic, and by adding constraint forces we model incompressible flow. The key tools used are the interconnection maps relating the dynamics of fluid motion to the dynamics of advected quantities.
AB - Part I of this paper presented a systematic derivation of the Stokes Dirac structure underlying the port-Hamiltonian model of ideal fluid flow on Riemannian manifolds. Starting from the group of diffeomorphisms as a configuration space for the fluid, the Stokes Dirac structure is derived by Poisson reduction and then augmented by boundary ports and distributed ports. The additional boundary ports have been shown to appear naturally as surface terms in the pairings of dual maps, always neglected in standard Hamiltonian theory. The port-Hamiltonian model presented in Part I corresponded only to the kinetic energy of the fluid and how its energy variables evolve such that the energy is conserved. In Part II, we utilize the distributed port of the kinetic energy port-Hamiltonian system for representing a number of fluid-dynamical systems. By adding internal energy we model compressible flow, both adiabatic and isentropic, and by adding constraint forces we model incompressible flow. The key tools used are the interconnection maps relating the dynamics of fluid motion to the dynamics of advected quantities.
KW - UT-Hybrid-D
KW - math-ph
KW - math.DG
KW - math.MP
KW - physics.flu-dyn
U2 - 10.1016/j.geomphys.2021.104199
DO - 10.1016/j.geomphys.2021.104199
M3 - Article
SN - 0393-0440
VL - 164
JO - Journal of geometry and physics
JF - Journal of geometry and physics
M1 - 104199
ER -